Step by step
The question
Question: graph x + 2y ≤ 4 and y > x − 2.
We shade the answer of each one.
Where both are shaded, both are true.
1 Crossing points of ①
On the x-axis, y = 0.
Put 0 in place of y.
2 times 0 is 0.
Adding 0 changes nothing.
So x = 4.
On the y-axis, x = 0.
Put 0 in place of x.
0 plus 2y is just 2y.
2y means 2 times y.
We want just y.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just y is left.
4 divided by 2 is 2.
So y = 2.
So line ① crosses the axes at (4, 0) and (0, 2).
2 Graph ①
Draw the grid.
①: The sign has "or equal to".
So the line is solid.
Put the two crossing points on the grid,
and join them: solid.
Which side?
We test one point: (0, 0).
Put x = 0 and y = 0 into ①.
Is 0 less than or equal to 4?
Yes, true.
So we shade the side with (0, 0), in red.
3 Graph ②
②: The sign is more than, with no "or equal to".
So the line is dashed.
b = −2.
Start on the y-axis at −2.
m = 1.
Go right 1,
then up 1.
Dot.
Join the dots: dashed.
Which side?
We test one point: (0, 0).
Put x = 0 and y = 0 into ②.
Is 0 more than −2?
Yes, true.
So we shade the side with (0, 0), in blue.
4 Where both are shaded
This part is shaded twice.
It is the answer.
Careful!
The answer is not everything we shaded.
Only the part shaded twice works in both.
5 Check
Let's check with a point in the purple part: (−1, −1).
Put it into ①.
Now ②.
True in both!
So the answer is right.
Let's look back.
First: crossing points of ①.
Then: graph ①.
Then: graph ②.
Then: where both are shaded.
Last: check.